Why would a dog show submissive behavior when he is petted?

Dogs crave attention. They also love to be scratched in some places more than others, like behind the ears and under the chin.

Because it shows that you are giving them affection; plus, it feels good to them.

.... Think of it as if you were a kid again, and your mother, father, guardian, girlfriend, or boyfriend let you lay your head on their lap as you lay down and they ran their fingers through your hair, it just feels good